Target Test Prep EA Quant Challenge Problem 3

Solution:

Question Stem Analysis:

If we let x = the number of cases of red wine sold, the revenue from red wine can be expressed as rx. Similarly, if we let y = the number of cases of white wine sold, the revenue from white wine can be expressed as wy. Thus, the ratio we're looking for is

$\Rightarrow \frac{\text{revenue from red wine}}{\text{revenue from white wine}}=\frac{\mathrm{r}\mathrm{x}}{\mathrm{w}\mathrm{y}}$

Remember that we'll need to produce a constant ratio in order to produce a meaningful ratio.

Statement One Alone:

$\Rightarrow$ Last Sunday, the Stewart Vineyard sold each case of red wine for 3 times as much as each case of white wine.

This means that r = 3w, which we can substitute for r in our ratio:

$\Rightarrow \frac{\text{revenue from red wine}}{\text{revenue from white wine}}=\frac{3\mathrm{w}\mathrm{x}}{\mathrm{w}\mathrm{y}}=\frac{3\mathrm{x}}{\mathrm{y}}$

This is not sufficient because there are still two different variables in the fraction. Different values of x and y would change the value of the fraction. Statement one alone is not sufficient.

Eliminate answer choices A and D.                                              

Statement Two Alone:

$\Rightarrow$ Last Sunday, the Stewart Vineyard sold 2 times as many cases of white wine as it sold of red wine.

This means that y = 2x, which we can substitute for y in our ratio:

$\Rightarrow \frac{\text{revenue from red wine}}{\text{revenue from white wine}}=\frac{\mathrm{r}\mathrm{x}}{\mathrm{w}2\mathrm{x}}=\frac{\mathrm{r}}{2\mathrm{w}}$

This ratio is not sufficient because there are two different variables in the fraction. Different values of r and w would change the value of the fraction. Statement two alone is not sufficient.

Eliminate answer choice B.

Statements One and Two Together:

Substituting the information from both statements for variables in our original ratio, we can produce the following fraction:

$\Rightarrow \frac{\text{revenue from red wine}}{\text{revenue from white wine}}=\frac{3\mathrm{w}\mathrm{x}}{\mathrm{w}2\mathrm{x}}=\frac{3}{2}$

Thus, the ratio of revenue from red wine to revenue from white wine is 3:2. Statements one and two together are sufficient to answer the question.